r(s+t)=u

options:


t=u−s/r



t=u/r−s



t=u/r+s



t=ru−s

Answer:

Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)]h

Where, l is the lower limit of the modal class

f₁ is the frequency of the modal class

f₀ is the frequency preceding the modal class

f₂ is the frequency succeeding the modal class

h is the class size

From the table,

Maximum frequency = 41

This frequency lies in the class 10000 - 15000

l = 10000

h = 5000

f₁ = 41

f₀ = 26

f₂ = 16

Now, f₁ - f₀ = 41 - 26 = 15

2f₁ - f₀ - f₂ = 2(41) - 26 - 16

= 82 - 42

= 40

[(f₁ - f₀)/(2f₁ - f₀ - f₂)] = 15/40

= 3/8

Now, mode = 10000 + (3/8)(5000)

= 10000 + (15000/8)

= 10000 + 1875

= 11875

Total sales during the last 6 months ≈ $330,250. It appears that more sales were made during the last half of the year. Estimated total sales during the last 6 months = $330,250

As per the given graph, we can estimate the total sales during the first 6 months and the last 6 months by calculating the area under the curve for the respective time intervals.

Using the trapezoidal rule, we can approximate the area under the curve for each time interval by summing the areas of trapezoids formed by adjacent data points.

(a) Using the given data points, we can calculate:

Total sales during the first 6 months ≈ $315,750

Total sales during the last 6 months ≈ $330,250

(b) Based on the above estimates, it appears that more sales were made during the last half of the year.

(c) Estimated total sales during the first 6 months = $315,750

Estimated total sales during the last 6 months = $330,250

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Answer: I believe the answer would be 12

Step-by-step explanation:

The answer comes out as 11.8 so the answer should be 12

thirty-two thousandths is the same as 0.032.

In order to determine

Answer:  y = 1.2x + 1.4

Step-by-step explanation:

1. Write down the coordinates of the first point. Let's assume it is a point with x₁ = -2and y₁ = -1.

2. Write down the coordinates of the second point as well. Let's take a point with x₂ = 3 and y₂ = 5.

3. Use the slope intercept formula to find the slope:

m = (y₂ - y₁)/(x₂ - x₁) = (5-1)/(3-2) = 4/1 = 1.2

4. Calculate the y-intercept. You can also use x₂ and y₂ instead of x₁ and y₁ here.

b = y₁ - m * x₁ = -1 - 1.2*-2 = 1.4

5. Put all these values together to construct the slope intercept form of a linear equation:

y = 1.2x + 1.4

Answer:

-9

Step-by-step explanation:

-4+4-9 ( remove the opposites)

-9 ( answer)

Hope its help you

Answer:

It would take 3 minutes

Step-by-step explanation:

A homogeneous system in parametric vector form:

(x1,x2,x3) = (s,s,-0.25s)

Parametric vector Form:

Any equation expressed as a parameter is a parametric equation. The general equation y = mx + b (where m and b are parameters) of a straight line in the form of a slope intersection is an example of a parametric equation. Example: one of the variables to t(x = t). Then we can rewrite this equation as y = t²+5.

So the set of parametric equations is x = t and y=t²+5.

According to the Question:

We are to solve them in parametric form.

X₁ + 2X₂ + 12X₃ = 0     ----------------------- (1)

2X₁ + X₂ + 12X₃ = 0     ----------------------- (2)

-X₁ + X₂ = 0                  ----------------------- (3)

From equation 3 we get

x₁ = x₂

Substitute in 1 and 2 to get

3x₁ + 12x₃ = 0 and

3x₁ + 12x₃ = 0

Thus, we find these two equations are dependent.  So we can have infinite solutions in parametric form only.

No unique solution is possible

Let x₁ = x₂ = s

Since 3x₁ +12x₃ = 0

x₁ = -4x₃

Or x₃ = -0.25s

So solution in parametric form is

(x1,x2,x3) = (s,s,-0.25s) for all real values.

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The acid test ratio of the company is 2.19 .

Given,

Company's creditors,  stock, debtors, overdraft , cash  expenses .

So,

Current assets = Stock + Debtors + Cash

Current assets = $5,450 + 10,620 + 3,400 = $19,470

Current liabilities = Creditors + Overdraft

Current liabilities = $4,300 + 2,100 = $6,400

Current ratio = Current assets / Current liabilities

Current ratio = $19,470 / $6,400 = 3.04

Acid test ratio = Current assets - Stock / Current liabilities

Acid test ratio = $19,470 - 5,450 / $6,400

Acid test ratio = $14,020 / $6,400 = 2.19

Hence option B is correct.

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Table of the question:

Solve for dy/dx:   dy/dx = (-2x) / (2y) = -x / y which gives the slope of tangent line using implicit differentiation

To find the slope of a tangent line using implicit differentiation, follow these steps:

1. Start with the given equation that represents the relationship between x and y in the form of an equation involving both variables, for example: F(x, y) = 0.

2. Differentiate both sides of the equation with respect to x using the chain rule whenever necessary. Treat y as a function of x and apply the derivative rules accordingly.

3. After differentiating, have a resulting equation involving both x, y, and their derivatives (dy/dx). Rearrange the equation if necessary to isolate dy/dx on one side.

4. Solve for dy/dx to find the derivative of y with respect to x. This will give the slope of the tangent line at any given point on the curve defined by the implicit equation.

Note: The resulting expression for dy/dx may involve both x and y variables. To find the slope of the tangent line at a specific point, substitute the coordinates of that point into the expression for dy/dx.

Here's an example to illustrate the process:

Given the implicit equation: \(x^2 + y^2 = 25\)

1. Start with the equation: \(x^2 + y^2 = 25.\)

2. Differentiate both sides with respect to x:

  2x + 2y * (dy/dx) = 0

3. Rearrange the equation to isolate dy/dx:

  2y * (dy/dx) = -2x

4. Solve for dy/dx:

  dy/dx = (-2x) / (2y)

         = -x / y

Now, have the expression for the slope of the tangent line in terms of x and y. To find the slope at a specific point, substitute the coordinates of that point into the expression.

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(a) To show that y(t) = ᵗ∫₀ e⁻ᵘ² du satisfies the initial value problem dy/dt = e⁻ᵗ², y(0) = 0, we differentiate y(t) with respect to t and substitute the given differential equation and initial condition.

(b) To approximate the integral ²∫₀ e⁻ᵘ² du using the Euler Method with h = 1/2, we divide the interval [0, 2] into subintervals of width h and approximate the integral using the formula: ∑[f(u(i))*h], where f(u(i)) represents the function evaluated at each subinterval.

(a) To show that y(t) = ᵗ∫₀ e⁻ᵘ² du satisfies the initial value problem dy/dt = e⁻ᵗ², y(0) = 0, we first differentiate y(t) with respect to t. Using the Fundamental Theorem of Calculus, we have:

dy/dt = d/dt [ᵗ∫₀ e⁻ᵘ² du]

Applying the Leibniz rule for differentiating under the integral sign, we obtain:

dy/dt = ∫₀ e⁻ᵘ² du

Now we substitute the given differential equation dy/dt = e⁻ᵗ² and the initial condition y(0) = 0:

e⁻ᵘ² = e⁻ᵗ²

Since e⁻ᵘ² and e⁻ᵗ² are equal, the given function y(t) = ᵗ∫₀ e⁻ᵘ² du satisfies the initial value problem.

(b) To approximate the integral ²∫₀ e⁻ᵘ² du using the Euler Method with h = 1/2, we first divide the interval [0, 2] into subintervals of width h = 1/2. In this case, we will have four subintervals: [0, 1/2], [1/2, 1], [1, 3/2], and [3/2, 2].

Using the Euler Method, we approximate the integral within each subinterval by evaluating the function e⁻ᵘ² at the left endpoint of the subinterval and multiplying it by the width of the subinterval. Then, we sum up these approximations for all subintervals.

For example, in the first subinterval [0, 1/2], the approximation would be:

Approximation for

[0, 1/2] = e⁻⁰² * (1/2) = (1/2)

Similarly, we can calculate the approximations for the other subintervals:

Approximation for

[1/2, 1] = e⁻¹/₂² * (1/2) ≈ (0.60653/2)

Approximation for

[1, 3/2] = e⁻¹² * (1/2) ≈ (0.13534/2)

Approximation for

[3/2, 2] = e⁻³/₂² * (1/2) ≈ (0.18394/2)

Finally, we sum up these approximations:

Approximation for

²∫₀ e⁻ᵘ² du ≈ (1/2) + (0.60653/2) + (0.13534/2) + (0.18394/2)

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4x - 9 = -2x + 9

collect like term

4x + 2x = 9 + 9

6x = 18

Divide both-side of the equation by 6

x = 18/6

x = 3

The upper bound of the 98% confidence interval for customer spending will be less than $55.

To find the upper bound of the 98% confidence interval for customer spending, we can use the fact that the confidence interval is symmetrical around the sample mean.

Given that the 99% confidence interval for customer spending is ($9, $32), we know that the sample mean lies at the center of this interval. Let's denote the sample mean as "\(\bar X\)".

The midpoint of the confidence interval is the average of the upper and lower bounds. Since the sample mean lies at the midpoint, we have:

(\(\bar X\) + $9) / 2 = $32

Simplifying the equation, we have:

\(\bar X\) + $9 = 2 * $32

\(\bar X\) + $9 = $64

Subtracting $9 from both sides:

\(\bar X\) = $64 - $9

\(\bar X\) = $55

Therefore, the sample mean is $55.

To find the upper bound of the 98% confidence interval, we need to determine the range between the sample mean and the upper bound of the 99% confidence interval.

The range of the 99% confidence interval is $32 - $55 = -$23.

Since the 98% confidence interval is narrower, the range will be smaller than -$23.

To find the upper bound of the 98% confidence interval, we subtract this range from the sample mean:

Upper bound = $55 - (smaller range)

As we don't have the specific value of the smaller range, we cannot determine the exact upper bound without additional information.

However, we can conclude that the upper bound of the 98% confidence interval for customer spending will be less than $55.

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The correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A positive correlation means that as one variable (in this case, happiness) increases, the other variable (GPA) also tends to increase. The magnitude of the correlation coefficient, which ranges from -1 to 1, represents the strength of the relationship. A value of 0.90 indicates a very strong positive linear correlation, suggesting that there is a consistent and significant relationship between happiness and GPA.

This means that as the level of happiness increases among high school students, their GPA tends to be higher as well. The correlation coefficient of 0.90 suggests a high degree of predictability in the relationship between these two variables.

It is important to note that correlation does not imply causation. While a strong positive correlation indicates a relationship between happiness and GPA, it does not necessarily mean that one variable causes the other. Other factors or variables may also influence the relationship between happiness and GPA.

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50% of Susan's trips to class would take more than 50 minutes.Answer: 50%.

Given data: The average time it takes for Susan to get to her class is 50 minutes. And the standard deviation is 5 minutes. We have to find the proportion of Susan's trips to class would take more than 50 minutes.

Solution:To find out the required proportion, we need to calculate the Z-score first.

\(Z-score = (X - μ)/σ\)

where, X = the value of the random variable (Susan's time to get to class)

μ = the population mean (average time)σ = the standard deviation

Here, X = 50 minutes

μ = 50 minutes

σ = 5 minutes

Z-score = (X - μ)/σ

= (50 - 50)/5

= 0

The Z-score table indicates that the area under the standard normal distribution curve for a Z-score of 0 is 0.5. Therefore, 50% of Susan's trips to class would take more than 50 minutes.Answer: 50%.

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Answer:

linear.

rotary.

reciprocating.

oscillating.

hope it wil help you

a.  the value of P(2.4 < x < 3) is 8.1.

b. the value of E(X) is 10.

Given function is f(x) = 5(6)x for x≥1 and elsewhere for a continuous random variable z.  

a. Compute P(2.4 < x < 3)

For continuous random variable, P(a < x < b) = ∫f(x)dx, where f(x) is the probability density function (PDF).

Here, f(x) = 5(6)x for x≥1 and elsewhere

So, P(2.4 < x < 3) = ∫f(x)dx = ∫2.4^35(6)xdx= 5 ∫2.4^36xdx= 5 [(3^2 - 2.4^2)/2] = 5 [(9 - 5.76)/2] = 5 [1.62] = 8.1

Hence, the value of P(2.4 < x < 3) is 8.1.

b. Compute E(X)Expected value of X is given by E(X) = ∫xf(x)dxFor continuous random variable, E(X) = ∫xf(x)dx, where f(x) is the probability density function (PDF).Here, f(x) = 5(6)x for x≥1 and elsewhereSo, E(X) = ∫xf(x)dx = ∫1∞5(6)x.xdx+ ∫-∞0 0dx= 5 ∫1∞6x^2dx+ 0 = 5 [(6) (x^3)/3]1∞= 5 [(6) (1^3)/3] = 10

Hence, the value of E(X) is 10.

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Given f(x)= 5 (6) x for rexeh 1 o elsewhere for a continuous veidon variable z. We are required to compute p(2.4 < x <3) and E(x).

Compute p(2.4 < x <3)For the given function, f(x) = 5 (6) x for 1 ≤ x ≤ 3 and 0 elsewhere.

So, the total area under the curve will be equal to 5 (6) 2 = 60.

And the required probability is given by the area under the curve from 2.4 to 3.  [Illustration is provided below]

Hence, p(2.4 < x <3) = 3.6

(b)Compute E(x)Expected value of x, E(x) is given by E(x) = ∫xf(x) dx,

which is equal to the area under the curve multiplied by the distance over which the function is spread.

Let's calculate the area under the curve, which is equal to 60, as we have calculated earlier.

Now, we calculate the distance over which the function is spread.

Distance = 3 - 1 = 2 unitsHence, E(x) = 60/2 = 30.

Answer:Therefore, p(2.4 < x <3) = 3.6 and E(x) = 30.

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Answer:

c

Step-by-step explanation:

you want to take your total amount of points and divide it by the number of games

Answer:

C. 3.25

Step-by-step explanation:

:)

The correct answer is  you will get approximately £1.30 for one Australian dollar.

To find out how many British pounds you will get for one Australian dollar, we need to determine the exchange rate between the British pound and the Australian dollar.

Given that £1 = US$1.11316 and A$1 = US$0.8558, we can calculate the exchange rate between the British pound and the Australian dollar as follows:

£1 / (US$1.11316) = A$1 / (US$0.8558)

To find the value of £1 in Australian dollars, we can rearrange the equation:

£1 = (A$1 / (US$0.8558)) * (US$1.11316)

Calculating this expression, we get:

£1 ≈ (1 / 0.8558) * 1.11316 ≈ 1.2992

Therefore, you will get approximately £1.30 for one Australian dollar.

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The equations of the planes that are parallel to the plane x 2y−2z = 1 and two units away from it is x + 2y - 2z = 3.

The coefficients of x, y, and z in the equation x+2y-2z=1 give us the normal vector of the plane, which is <1, 2, -2>.

We can choose any point on the given plane as a point on the parallel plane. For simplicity, we can use the point (1,0,0), which is on the given plane.

The point-normal form of the equation of a plane is given by: a(x-x0) + b(y-y0) + c(z-z0) = 0, where (x0, y0, z0) is a point on the plane, and <a, b, c> is the normal vector of plane.

Since we want a plane that is two units away from given plane, we can modify the constant term in the equation to get: a(x-x0) + b(y-y0) + c(z-z0) = d, where d is the distance between two planes, which is 2 units in this case.

The equation of the parallel plane is:

Normal vector of the given plane: <1, 2, -2>

Point on the given plane: (1,0,0)

Distance between the two planes: 2 units

Using the point-normal form:

1(x-1) + 2(y-0) - 2(z-0) = 2

Simplifying:

x + 2y - 2z = 3

Therefore, the equation of a plane that is parallel to the plane x+2y-2z=1 and two units away from it is x + 2y - 2z = 3.

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Answer:

128°

Step-by-step explanation:

the answer is 128° i explained it as i could in the diagram hope you understand

Answer:

YES
....................................

The series after solving the following term f(x) = \(e^{-2x}\) is given as:

\(e^{-2x}\) = 1 - 2x + 2x² - 4/3x³ + 2/3x⁴ - 4/15x⁵+....|x| < ∞.

The fundamental concepts in mathematics are series and sequence. A series is the total of all components, but a sequence is an ordered group of items in which repeats of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.

By using the formulae to solve issues, one may gain a deeper understanding of the principles. The main distinction between them and sets is that in a sequence, certain terms might appear again in different locations. A series can be finite or infinite in length and has length equal to the number of terms.

Given f(x) = \(e^{-2x}\), center x = 0

f(x) = \(e^{-2x}\) = \(1 - 2x + \frac{(2x)^2}{2!} +\frac{(2x)^3}{3!} +\frac{(2x)^4}{4!} +\frac{(2x)^5}{5!} +.....|x|\)

\(e^{-2x}\) = 1 - 2x + 4(\(\frac{x^2}{2}\)) - 8(\(\frac{x^3}{6}\)) + 16(\(\frac{x^4}{24}\)) - 35(\(\frac{x^5}{100}\))+.....|x| < ∞

\(e^{-2x}\) = 1 - 2x + 2x² - 4/3x³ + 2/3x⁴ - 4/15x⁵+....|x| < ∞

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Answer: B

explanation: I took the test ^w^

If Nina babysat for 5 hours,  then she earn 141 of money and option B choice correctly identifies the extraneous information in the problem

Two or more expressions with an Equal sign is called as Equation.

Given that Anna babysat 2 children on Saturday night.

She charges $8 an hour to babysit

She wants to save the money she earns babysitting to buy a stereo system that cost $225

If Nina babysat for 5 hours,  then we need to find how much money money did she earn.

8/225=5/x

Apply cross multiplication

8x=225(5)

8x=1125

x=1125/8

x=140.6=141

Hence, If Nina babysat for 5 hours,  then she earn 141 of money and option B choice correctly identifies the extraneous information in the problem

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Step-by-step explanation:

3x + 8y + 5

The true statements

5 is a constant

3x + 8y + 5 is written as a sum of three terms

3x and 5 are like terms

Answer:

a) 2(x+4)

b) 3(x-4)

c) 2(3x+2)

d) 9(2x-1)

Step-by-step explanation:

a) 2x+8=2(x+(8/2))=2(x+4)

b) 3x-12=3(x-(12/3))=3(x-4)

c) 6x+4=2((6/2)x+(4/2))=2(3x+2)

d) 18x-9=9((18/9)x-(9/9))=9(2x-1)

Answer:

a) 2(x + 4)

b) 3(x -4)

c) 2(3x + 2)

d) 9(2x - 1)

Step-by-step explanation:

a) Factor: 2x+8

   2x + 8

= 2(x + 4)

b) Factor 3x−12

   3x − 12

= 3(x − 4)

c) Factor 6x+4

   6x + 4

= 2(3x + 2)

d) Factor 18x−9

   18x − 9

= 9(2x − 1)

Answer:

3.2

Step-by-step explanation:

Answer:

pythagorean theorem !!!!!!

Step-by-step explanation:

0.8²+1.6²=3.2²

0.64+2.56=10.24

THAT means the distance is

\( \sqrt{10.24} \)

=3.2miles